Creating a hole out of an custom shape
To model a hole you will have to engineer a vertex by having an edge perpendicular to the edge shown. There are other options such as a bool. The main issue I can see here is that the surrounding topology could be better and any cuts would distort what you have due to the curves in the object.

Here is an option if you have a vert and I have shown it on a simple plane. You can take the process and do the same on yours but will need that edge crossing to create a vert.

Select the vertex



Ctrl + shift + b to bevel the vertex with 2 segments



Roughly get the shape of a circle.

Select the faces and right click to get your loop tools. If you do not have loop tools then get them via preferences add on (they come with Blender). Very useful to have if they are not already there.

With loop tools select circle and that will make your shape more circular





select i for inset and make a small inset to create a supporting edge for your circle and then delete the inner faces. Add the edge cuts (knife) to create quads.



With a sub surface modifier x 2 you get



Your issue here is getting that vertex. You could try this but I suspect it will distort at the bottom of the shape. Maybe it is worth a go but most options from here will probably distort a bit due to the existing topology.